Question: Solve for $r$. $12-\dfrac15r=2r+1$ $r=$
We need to manipulate the equation to get $ r $ by itself. $\begin{aligned} 12-\dfrac15r&=2r+1 \\\\ 12-\dfrac15r {-2r} &= 2r+1{-2r} &&\gray{\text{Subtract 2r from each side.}}\\\\ -\dfrac{11}5r+12&=1 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac{11}5r+12{-12} &= 1{-12} &&\gray{\text{Subtract 12 from each side.}}\\\\ -\dfrac{11}5r &=-11 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac{11}{5}r\cdot\left({-\dfrac{5}{11}}\right) &= -11\cdot\left({-\dfrac{5}{11}}\right) &&\gray{\text{Multiply each side by -}\dfrac{5}{11}.}\\\\ r&=\dfrac{55}{11}\\\\\\ r &= {5} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $r = {5 }~~~~~~~~$ [Let's check our work!]